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Let $ω : (0, \infty) \to (0, \infty)$ be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure $μ \in ℝ^{n}$ is called $ω$ -Zygmund if there exists a positive constant $C$ such that $| μ (Q_{+}) - μ (Q_{-}) | \leq C ω (ℓ (Q_{+})) | Q_{+} |$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size. Similarly, $μ$ is called an $ω$ - symmetric measure if there exists a positive constant $C$ such that $| μ (Q_{+}) / μ (Q_{-}) - 1 | \leq C ω (ℓ (Q_{+}))$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size, $ℓ (Q_{+}) = ℓ (Q_{-}) < 1$ . We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...

The absolute continuity of functions defined on the $σ$ -ring generated by a ring

Mária Pastorová (1978)

Mathematica Slovaca

The chain rule for differentiable measures

Hui-Hsiung Kuo (1978)

Studia Mathematica

The converse of the Fatou theorem for smooth measures.

Dubtsov, E.S. (2004)

Zapiski Nauchnykh Seminarov POMI

The hardy-littlewood maximal function and derivation of integrals.

Baldomero Rubio (1975)

Collectanea Mathematica

The property of weak type (p,p) for the Hardy-Littlewood maximal operator and derivation of integrals

Baldomero Rubio (1976)

Studia Mathematica

The Radon--Nikodym theorem for reflexive Banach spaces.

Bárcenas, Diómedes (2003)

Divulgaciones Matemáticas

To the problem of a strong differentiability of integrals along different directions.

Lepsveridze, G. (1998)

Georgian Mathematical Journal

Uniform distribution preserving mappings

R. F. Tichy, R. Winkler (1991)

Acta Arithmetica

Upper and lower Lebesgue-Stieltjes integrals

D. Dutta (1975)

Fundamenta Mathematicae

Variational measures in the theory of the integration in $ℝ^{m}$

Luisa Di Piazza (2001)

Czechoslovak Mathematical Journal

We study properties of variational measures associated with certain conditionally convergent integrals in $ℝ^{m}$ . In particular we give a full descriptive characterization of these integrals.

Vitali Lemma approach to differentiation on a time scale

Chuan Jen Chyan, Andrzej Fryszkowski (2004)

Studia Mathematica

A new approach to differentiation on a time scale is presented. We give a suitable generalization of the Vitali Lemma and apply it to prove that every increasing function f: → ℝ has a right derivative f₊’(x) for $μ_{Δ}$ -almost all x ∈ . Moreover, $\int_{[a, b)} f ₊^{'} (x) d μ_{Δ} \leq f (b) - f (a)$ .

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Sulla disintegrazione delle misure negli spazi localmente compatti

Sull'additività dell'integrale

Sur les fonctions approximativement continues

Symmetric and Zygmund measures in several variables

The absolute continuity of functions defined on the $σ$ -ring generated by a ring

The chain rule for differentiable measures

The converse of the Fatou theorem for smooth measures.

The hardy-littlewood maximal function and derivation of integrals.

The property of weak type (p,p) for the Hardy-Littlewood maximal operator and derivation of integrals

The Radon--Nikodym theorem for reflexive Banach spaces.

To the problem of a strong differentiability of integrals along different directions.

Uniform distribution preserving mappings

Upper and lower Lebesgue-Stieltjes integrals

Variational measures in the theory of the integration in $ℝ^{m}$

Vitali Lemma approach to differentiation on a time scale

Vitali Systems in Rn with Irregular Sets.

Vitali type theorems for a class of measures in R...

Weak type estimates for the Hardy-Littlewood maximal functions

Zur Integrationstheorie über bewerteten Körpern und der Darstellung des Biduals von ... (X, ...).

Аппроксимационные и дифференциальные свойства измеримых множеств

Currently displaying 81 – 100 of 106